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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 116 pdf
... change with constant rate of change, 712–714 difference between left- and right-hand sums and, 718–722 explanation of, 712 with nonconstant rate of change, 715–718 overview of, 711–712 Newton, ... integrals explanation of, 903 infinite interval of integration and, 903–907 method of comparison and, 912–914 methods to approach, 908–912 unbounded and discontinuous integrands and, 907–908 use of, 903 ... functions, 334–338 historical background of, 211 instantaneous rate of change and, 209–211, 711, 983 of inverse trigonometric functions, 703–706 limit definition of, 190, 191 local linearity and, ...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 1 pps
... Joan) Calculus: an integrated approach to functions and their rates of change / by Robin Gottlieb. Preliminary ed p cm ISBN 0-2 01- 70929-5 (alk paper) Calculus I Title QA303 G685 20 01 00-0 618 55 ... function and its derivative without being formally introduced to the derivative Part II focuses on rates of change and modeling using linear and quadratic functions Linearity and interpretation of ... course, at the instructor’s discretion Part I provides an introduction to functions and their representations with an emphasis on the relationship between meaning and symbolic and graphic representations...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 2 ppsx
... Functions 421 Inverse Functions: Can What Is Done Be Undone? 421 12. 1 What Does It Mean for f and g to Be Inverse Functions? 12. 2 Finding the Inverse of a Function 429 12. 3 Interpreting the Meaning of ... and Arc Lengths 619 CHAPTER 20 Trigonometry—Circles and Triangles 627 20 .1 Right-Triangle Trigonometry: The Definitions 20 .2 20.3 20 .4 20 .5 Triangles We Know and Love, and the Information They Give ... Limits and Continuity 24 5 7.1 7 .2 Investigating Limits—Methods of Inquiry and a Definition 24 5 Left- and Right-Handed Limits; Sometimes the Approach Is Critical 7.3 7.4 N CHAPTER 22 6 A Streetwise Approach...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 3 ppsx
... important and versatile We can attach many different mental pictures and representations to it; our choice of representation will often depend upon context Upon first exposure, the notation and ... output of f corresponding to an input of x” and it is read “y equals f of x.” When we say y = f (x), we mean that y depends on x and is uniquely determined by x N EXAMPLE 1.2 Functional notation and ... 1.2 What Are Functions? Basic Vocabulary and Notation A is a function with domain {1, 2, 3, 4, 5} and range {c, d, g, o, s}.4 B is a function with domain {1, 2, 3, 4, 5, 6} and range {c, d} C...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 4 doc
... price of a car and let f and g be the tax functions in states and 2, respectively We can describe the input-output relationship of the functions f and g using formulas f (x) = 500 g(x) = 0.04x The ... undefined; Equality of Functions The functions f and g are equal if: f and g have the same domain, and f (x) = g(x) for every x in the domain −x For example, the functions f (x) = x x and g(x) = x − ... at and 5 (2, 5) denotes the set of all numbers greater than and less than but excluding and themselves x ∈ (2, 5) is equivalent to < x < (2, 5) is called an open interval because neither of its...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 5 pptx
... a panda needs to take in C calories for every pound of the panda’s weight i The number of pounds of sugar cane it takes to support a panda for a day is a function of the weight, x, of the panda ... discussions, so we’ll pause for a moment to clarify the meaning of an “if and only if” statement Language and Logic: An Interlude “A if and only if B” means “A and B are equivalent statements.” Using ... constants S, N, and C ii The number of pounds of sugar cane it takes to support a pair of pandas, one weighing P pounds and the other weighing Q pounds, for a period of W weeks is a function of...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 6 doc
... rectangular box has a square base Let s denote the length of the sides of the base and let h denote the height of the box, s and h in inches (a) Express the volume of the box in terms of s and ... Consider the functions f , g, h, and k presented as graphs in Problems through 11 Which, if any, of these functions are 1 -to- 1? 38 CHAPTER Functions Are Lurking Everywhere 13 The graphs of f and g are ... graph of a function? y y (a) y y (b) (c) (d) x x x x Figure 1.18 Answer We can tell that the relationships represented in Figures 1. 16( a)–(c), 1.17(a) and (b), and 1.18(b) and (d) are, in fact, functions...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 7 pps
... answers to parts (a) and (b) in terms of any or all of the constants A, X, B, L, and C (a) Express the number of bushels of huckleberries the two bears eat as a function of t, the number of hours ... the manufacturer decides to switch to plastic lids and bottoms to eliminate the taping problems Assume that custom-made plastic lids and bottoms cost 7k cents per square inch Express the cost of ... amount of gravel in the pile as a function of its (a) height (b) radius 1.3 Representations of Functions 45 50 In Durham, England, the circular plots of land at the center of the roundabouts 17 are...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 9 potx
... 0) and decreasing on (0, ∞) (d) j is undefined and discontinuous at x = (e) j is 1 -to- 1 Answers to Exercise 2.8 (a) g and h are even functions (b) f and j are odd functions (c) The graph of an ... Geometric Approach: |2x + 3| > |2x − (−3)| > (the distance between 2x and −3) > We’ll focus on 2x and solve for x later 68 CHAPTER Characterizing Functions and Introducing Rates of Change –6 –5 ... return to the four functions we introduced at the beginning of this section: f (x) = x, g(x) = x 2, h(x) = |x|, and j (x) = x (a) Which of functions f , g, h, and j are even? (b) Which of functions...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 10 pps
... price of a cup of coffee in Seattle from 1970 to 2000 (b) The percent increase in the price of a cup of coffee in Seattle from 1970 to 2000 (c) The average rate of change of the price of a cup of ... and (c).) (e) Illustrate your answers to parts (a), (b), and (c) by sketching f (x) and drawing secant lines whose slopes correspond to these average rates of change Answer the previous question ... Simplify your answer 80 CHAPTER Characterizing Functions and Introducing Rates of Change (d) [1, + h] (Show that your answer agrees with the answers you obtained in parts (a), (b), and (c).) (e)...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 11 doc
... amount functions and their corresponding rate functions EXERCISE 2.10 Oil is leaking from a point and spreading evenly in a thin, expanding disk We can measure the radius of the disk and want to ... error is to be drawn in by the shape of a graph and leap headlong into a tangled web of incorrect conclusions without stopping to look at the labeling of the axes of the graphs You can be misled ... Characterizing Functions and Introducing Rates of Change Exploratory Problems for Chapter Runners Early one morning three runners leave Washington State University in Pullman and run the Palouse Path11 joining...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 12 ppt
... details and a very readable account, consult The History of Mathematics: An Introduction, by David Burton, McGraw-Hill Companies, Inc 1997 17 Due in part to their methods of record keeping and their ... climate, the ancient Egyptians and Babylonians have left modern historians more evidence of their mathematical development than have the people of other ancient civilizations The writings of the Greek ... –20) 94 CHAPTER Characterizing Functions and Introducing Rates of Change (a) Describe the trip in words Include where the trip started and ended and how fast (and in what direction) we traveled...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 13 pdf
... corresponding to an input of x1 is the sum of f (x1) and g(x1) In terms of the graphs, the height of h at x1 is the sum of the heights of the graphs of f and g at x1 An analogous statement can be made ... We can say that S is equal to the composition of f and g Composition of functions is analogous to setting up functions as workers (or machines) on an assembly line If the output of g is handed ... the output of j is the quotient of the outputs of f and g The product is g(x) defined for any x in the domains of both f and g; the quotient is defined for any x in the domains of both f and g provided...
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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 14 ppsx
... h(x) = f (g(x)) and j (x) = g(f (x)) What are the domains of h and j ? 35 f (x) = x + and g(x) = 36 f (x) = x+2 √ x and g(x) = x − 118 CHAPTER Functions Working Together 37 f (x) = x and g(x) = −2x ... x−3 and g(x) = x In Problems 39 through 43, find (f + g)(x), (fg)(x), and domains f g (x), and find their 39 f (x) = ax + b and g(x) = cx + d 40 f (x) = 3x + and g(x) = 5x − 41 f (x) = 2x + and ... output of another function N EXERCISE 3.11 There are many ways of decomposing functions For instance, suppose h(x) = x2 + x2 + and we want to find f and g such that f (g(x)) = h(x) Determine which of...
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